Can vampires(and Serana since she is one) get pregnant? I dont understand the link between vampires and undead.

So if a living person gets infected or turned into a vampire, he is considered dead already? In that case dead people cannot have babies but what about when the person gets cured. He goes back into a living person and act like one?

I am asking it because i made a mistake and cured serana's vampirism. Now she is a living person after being dead for centuries?